To even pose the question of animal suffering is unique to humans. After all, it's only humans who create humane societies to advocate for animal welfare.
Why?
I don't know how others belief systems would explain that, but from a Christian perspective, humans aren't exactly the same as animals. We're like animals in that humans and animals are all creatures, and yet distinctly non-animal in that we're the only creatures made in the image of God, and given rule over all creature to promote the flourishing of life---human, animal, and plant---for God's glory. And the biblical story is that humans went so far off-course in rebellion against their Creator God that the Son of God had to become human, die, and rise again to restore our ability to care rightly for creation.
Thus, concerns to minimize animal suffering are uniquely human concerns because we /aren't/ animals, but human; and the concern itself is proof we're different from other animals.
Many animals are perfectly capable of understanding the suffering of other animals. It's illustrated by menu recorded instance of one animal helping other animals in need. Even of a different species. There's probably nothing unique about humans except slightly nimbler neurons.
As for the stories humans invented to explain their grace and their horribleness I can't say much. Only that we are very creative in that regard.
Why?
I don't know how others belief systems would explain that, but from a Christian perspective, humans aren't exactly the same as animals. We're like animals in that humans and animals are all creatures, and yet distinctly non-animal in that we're the only creatures made in the image of God, and given rule over all creature to promote the flourishing of life---human, animal, and plant---for God's glory. And the biblical story is that humans went so far off-course in rebellion against their Creator God that the Son of God had to become human, die, and rise again to restore our ability to care rightly for creation.
Thus, concerns to minimize animal suffering are uniquely human concerns because we /aren't/ animals, but human; and the concern itself is proof we're different from other animals.